The smart grid is envisioned to use a cyber-physical network paradigm to prevent failures from propagating along large-scale infrastructures, which is a primary cause for massive blackouts. Despite this promising vision, how effective cyber and physical interactions are against failure propagation is not yet fully investigated. In this paper, we use analysis and system-level simulations to characterize such interactions during load shedding, which is a process to stop failure propagation by shedding a computed amount of loads based on collaborative communication. Specifically, we model failures, such as system fault, happening in the physical domain as a counting process, with each count triggering a load shedding action in the cyber domain. Although global load shedding design is considered optimal by globally coordinating shedding actions, its induced failure probability (defined as the one that at least a given number of power lines fail) is shown scalable to the delay performance and the system size. This indicates that global load shedding is less likely to stop failure propagation in large systems than local shedding that sheds loads within a limited system scope. Our study demonstrates that a joint view on cyber and physical factors is essential for failure prevention design in the smart grid.